It's always difficult, my own perception of alphas would be somewhat complete, has the general gameplay loop, but still requires more features and still missing a lot of the final polishes. Beta is usually adding the polish and rarely ever new features. Prototypes, which is how I see your game personally, would be lacking most of the core mechanics and serve as testing smaller parts of the game.
It's also possible that I might be overestimating what the final product would be and you are aiming for something smaller. Which is good, I can only really get an understanding currently from the description of your game and what I played.
Regardless of what you choose to do, best of luck with it and hope it does well for your game!